Three-dimensional Finite Difference Research Articles

Ta<sub>2</sub>O<sub>5</sub> 980/1550 nm wavelength multiplexer/demultiplexer based on segmented cascaded multimode interference

On-chip erbium-doped/erbium-ytterbium co-doped waveguide amplifiers (EDWAs/EYCDWAs) have received extensive research attention in recent years, As an important component of EDWA, there has been relatively little research on integrated wavelength division multiplexing/demultiplexing devices for 980 nm pump light and 1550 nm signal light. This article aims to propose a compact Ta<sub>2</sub>O<sub>5</sub> 980 / 1550 nm wavelength diplexer based on multimode interference effects. The device employs a structure of symmetric interference and paired interference cascade, which reduces the total length of the segmented multimode interference waveguide to one-third of the ordinary paired multimode interference waveguide without using any complex structures such as subwavelength gratings to regulate the beat length of the pump and signal light. The three-dimensional finite difference time domain (3D-FDTD) tool was used to analyze and optimize the established model. The results demonstrate that the designed MMI diplexer has low insertion loss and high process tolerance, with an insertion loss of 0.4 dB at 980 nm and 0.8 dB at 1550 nm, and the extinction ratios are both better than 16 dB. Moreover, the 1-dB bandwidth is up to 150 nm around the 1550 nm wavelength and up to 70 nm around the 980 nm wavelength. The segmented structure designed in the article greatly reduces the design difficulty of MMI devices and reduces the overall size of 980 / 1550 nm wavelength division multiplexers/demultiplexers. It is expected to be applied in on-chip integrated erbium-doped waveguide amplifiers and lasers. In addition, the segmented design approach of cascading the hybrid multimode interference mechanism provides a technical reference for separating two optical signals with far apart center wavelengths such as 800 / 1310 nm and 1550 / 2000 nm, and has potential application value in communication and mid infrared diplexing devices.

Dynamic Response Mechanism of Bedding Slopes with Alternatively Distributed Soft and Hard Rock Layers Under Different Seismic Excitation Directions: Insights from Numerical Simulations.

The issue of slope stability in earthquakes has become increasingly prominent with the construction of many infrastructure projects such as highways, bridges, and tunnels. To explore the dynamic response characteristics of bedding rock slopes in an earthquake, the three-dimensional dynamic finite-difference method (TDD-FDM) in this study is used to establish simplified rock slope models, taking a bedding rock slope with alternatively distributed soft and hard rock layers in Yunnan, China as a prototype. The dynamic response mechanism of layered rock slopes containing different thicknesses, locations, and quantities of soft rock layers was studied under different excitation directions of seismic waves. The main findings are that the propagation of seismic waves at different rock layer structures has directionality, which causes the strongest seismic response to be all located in the upper or middle parts of the slope; the influence of rock structures on seismic response in layered rock slopes is in the order of thickness > quantity > location; the acceleration amplification effect of a slope under multi-directional seismic wave excitation exhibits the phenomena of differential amplification and coupling amplification; and the acceleration amplification factors of a slope with increasing peak ground acceleration from 0.05 g to 0.20 g show two trends: increasing-decreasing and continuous increasing. The findings of this study can be a reference for studying the dynamic response of rock slopes in strong earthquakes.

Binding Energy of Cylindrical Quantum Dots: Effects of External Electric Field and Impurity Position

We have investigated the binding energy properties of a cylindrical quantum dot (CQD) system layered as GaAs/AlGaAs under external electric fields. In our numerical calculations, we considered both on- and off-center impurity cases using the effective mass approximation. The eigenvalues and corresponding eigenfunctions of the system are obtained using a three-dimensional finite difference approach. It is found that the ground-state binding energy is significantly affected by the CQD dimensions (radius and height), impurity position, and the strength and direction of the external electric field. Additionally, the electron probability distributions are examined to provide deeper insight into the physical reasons underlying the behavior of the binding energy. These findings enhance our understanding of the tunable properties of CQDs, which may be useful in the design of optoelectronic and quantum devices.

Silver nanoparticles modified on cicada wings affect fluorescence and Raman signals based on electromagnetic and chemical enhancement mechanisms

The electromagnetic enhancement (EM) mechanism is one of the important theories that need to be mastered to study surface-enhanced fluorescence (SEF) and surface-enhanced Raman scattering (SERS). However, the charge transfer in the chemical enhancement (CM) mechanism has different effects on the two. The study developed a simple and environmentally friendly composite structural substrate by depositing silver (Ag) on the rough surface with regular columnar protuberances of bio-material cicada wings (CW) using magnetron sputtering technology. The formation of Ag nano-islands enhanced the fluorescence and Raman signals of rhodamine 6G (R6G), while the addition of silver nanoparticles (AgNPs) quenched the fluorescence. To explore the magical phenomenon, the electromagnetic field distribution on the surface of the substrate was simulated through three-dimensional finite difference time domain (3D-FDTD), which verified the experimental results of SEF and SERS. The results calculated by Gaussian16 with Density Functional Theory (DFT) and time-dependent density functional theory (TDDFT) explained the effect of adding AgNPs on the surface of the substrate on the fluorescence intensity. The work not only contributes experimental data and theoretical results to the EM mechanism and CM mechanism in enhanced spectra, but also provides ideas for preparing new SEF and SERS substrates.

A tunable narrow single-mode bandpass filter using graphene nanoribbons for THz applications

This paper presents a tunable, single-mode narrowband optical filter designed for terahertz applications utilizing graphene nanoribbons. To attain optimal conditions, the filter was devised in three steps. It is composed of two input and output waveguides and a T-shaped resonator with nanoscale dimensions. The transmission spectrum analysis employs the three-dimensional finite difference time domain and coupled mode theory methods. Tunability is achieved through the adjustment of the nanoribbon size and the chemical potential of graphene. The filter demonstrates remarkable performance metrics, including a maximum transmission spectrum efficiency of 99%, a full width at half maximum (FWHM) of 0.115 THz, a quality factor (Q-factor) of 100, and a free spectral range (FSR) of 45 THz. The presented structure holds significant promise for integrated optical components and compact optical devices, showcasing its applicability in the terahertz frequency range. Furthermore, the inherent sensitivity of this structure to changes in the refractive index of the substrate positions it as a potential sensor.

Numerical Modeling for Tunnel Lining Optimization

The construction of tunnels excavated by the conventional method in densely populated urban environments requires an adequate characterization of the loads acting on the primary lining during the excavation process, to ensure that the ground is deformed and stresses around the tunnel are relieved, simultaneously complying with the failure and serviceability limits of international standards while minimizing damage to nearby structures. In this paper, common lining design criteria are revisited, through the numerical simulation of an instrumented tunnel section which is part of a 4.5 km long metro line currently under construction in Mexico City. Key needs for improvement in current design approaches are identified. The tunnel was instrumented with load cells, extensometers, and topographical references for convergences and divergences. A three-dimensional finite difference model of the instrumented section was developed, and the load transfer mechanisms between the excavated soil and the primary lining were analyzed. Then, the numerical simulation of the contribution of the secondary lining in the overall stability for sustained load was established, along with the expected ground settlements, which can significantly affect nearby structures. Results gathered from this research are key for updating lining design criteria for urban tunnels built in stiff brittle soils.

Stability Analysis of Surrounding Rock and Initial Support of Tunnel Undercrossing Multi-Situational Goafs: A Reference of Construction Guidance

To ensure the construction and operational safety of tunnel undercrossing multi-situational goafs, the Huaying Mountain High-Speed Rail Tunnel, a critical section of the Xi’an-Chongqing High-Speed Railway, was taken as a case study. Based on a three-dimensional finite difference numerical simulation platform, twelve situations were established to analyze the effects of three factors: distance, scale, and angle. The stability analysis was conducted by examining the displacement and deformation characteristics of the surrounding rock, stress changes, and axial forces of the initial support for each situation. The results show that in tunnel undercrossing multi-situational goafs, the vertical deformation, horizontal convergence of the surrounding rock, and the maximum axial force of initial support are all affected. Within a certain range, changes in distance significantly impact subsidence and settlement deformation of the surrounding rock. However, as the distance increases, the horizontal and vertical displacements of the tunnel and the axial force of the initial support tend to decrease. Conversely, the scale and angle of the goaf have an opposite effect on the surrounding rock: as the scale and angle increase, the stability of the surrounding rock deteriorates. In this case study, when the distance exceeds 1.13 times the tunnel span, the influence of the goaf on the stability of the surrounding rock gradually decreases. When the angle exceeds 45°, vertical displacement decreases, and the increasing trend of horizontal displacement gradually diminishes. The conclusions of this paper can provide guidance for designing reinforcement schemes for tunnels crossing through multi-situational goafs. The findings provide valuable insights and guidance for similar engineering projects.

Simulation of coupled groundwater flow and contaminant transport using quintic B-spline collocation method

PurposeThe purpose of this study is to introduce a new numerical scheme with no stability condition and high-order accuracy for the solution of two-dimensional coupled groundwater flow and transport simulation problems with regular and irregular geometries and compare the results with widely acceptable programs such as Modular Three-Dimensional Finite-Difference Ground-Water Flow Model (MODFLOW) and Modular Three-Dimensional Multispecies Transport Model (MT3DMS).Design/methodology/approachThe newly proposed numerical scheme is based on the method of lines (MOL) approach and uses high-order approximations both in space and time. Quintic B-spline (QBS) functions are used in space to transform partial differential equations, representing the relevant physical phenomena in the system of ordinary differential equations. Then this system is solved with the DOPRI5 algorithm that requires no stability condition. The obtained results are compared with the results of the MODFLOW and MT3DMS programs to verify the accuracy of the proposed scheme.FindingsThe results indicate that the proposed numerical scheme can successfully simulate the two-dimensional coupled groundwater flow and transport problems with complex geometry and parameter structures. All the results are in good agreement with the reference solutions.Originality/valueTo the best of the authors' knowledge, the QBS-DOPRI5 method is used for the first time for solving two-dimensional coupled groundwater flow and transport problems with complex geometries and can be extended to high-dimensional problems. In the future, considering the success of the proposed numerical scheme, it can be used successfully for the identification of groundwater contaminant source characteristics.

Impacts of the mechanical connectors on seismic performance of the restored masonry Plaka Bridge using experimental and numerical studies

The use of clamp and dowel materials in the arch of the masonry bridges holds pivotal significance in enhancing the seismic resilience of these structures, as these elements contribute crucially to the structural integrity and dynamic response of these venerable structures. For this reason, the seismic performance of the restored historic Plaka Bridge, originally constructed in 1866 in Arta, Greece, and later restored in 2015 after flooding, was investigated considering the dowels and clamps in the arch section of this study. A combination of experimental and numerical analyses was conducted and verified to understand the in-situ interface behavior of the arch stones. In the first phase of the study, the mechanical properties of the dowels and clamps were characterized by the experimental tests. Compression and tension tests were conducted on the stone samples containing dowel bars and clamps respectively to determine the mechanical properties, The experimental outcomes were subsequently validated through Three-Dimensional (3D) Finite Difference Models (FDM). It was obtained that the dowels and clamps represent the bi-linear material model at the interfaces. Finally, the idealized interface behavior was constructed with normal and tangential spring stiffness properties in 3D-FD Models. These springs successfully simulate the interface delamination failure of the stones in all directions. In the final phase of the study, a 3D-FD model of the Plaka Bridge was constructed employing the previously validated normal and tangential stiffness elements in the arch of the bridge. A free-field non-reflecting boundary condition was imposed on the base and lateral boundaries of the bridge model. Seismic analyses were conducted utilizing the significant seismic events including 2023 Kahramanmaraş earthquakes. The results revealed significant alterations in the structural behavior of the bridge under considered earthquakes. Furthermore, the displacements, principal stresses and tensile-compressive damages in the main arch significantly reduced with the adopted stiffness values. This study proposes the undeniably realistic and efficient implementation of interface material modeling for the mechanical connections as opposed to the traditionally assumed mortar properties in literature. Furthermore, the combined behavior of the dowel, clamp, and Khorasan mortar proposes non-linear interface material model to the existing literature by invalidating commonly assumed linear interface behavior in masonry structures.

Thermotunable mid-infrared metamaterial absorption material based on combined hollow cylindrical VO2 structure

We have designed a metamaterial absorption material based on the VO2 phase transition effect. The aim is to realize thermally tunable broadband absorption in the mid-infrared band. The metamaterial absorption material is a three-layer structure. From top to bottom, the combined hollow cylindrical VO2 resonant layer, the SiO2 dielectric layer and the Ti substrate. In this work, we perform numerical simulations using the three-dimensional time-domain finite element difference method. The simulation shows that the absorption material's average absorption intensity is adjustable by temperature between 0.09 and 0.95. At a temperature of 342 K, the absorption material has an absorption bandwidth of 17.3 μm (6.43 μm to 23.73 μm) with an absorption rate above 90%. And the average absorption in this band range is 94.95%. And this band covers the wavelength of the atmospheric transparency window (8 μm∼14 μm), which suggests that our absorption material has great application prospects. In this work, we first analyze the electromagnetic field at the absorption material's resonant wavelength and explain the absorption material's absorption mechanism. Then, we investigated the absorption effect of the absorption material under the VO2 structure with different temperatures. And we explain temperature's effect on the absorption material's absorption effect by analyzing the electric field's change on the absorption material's surface at different temperatures for the same wavelength. The effect of the absorption material structural parameters on the absorption material absorption performance to determine the optimal structural parameters was then investigated. Finally, we investigate the absorption curves of the absorption material under different columnar VO2 layers and demonstrate the innovative and unique nature of the designed absorption material. The absorption material we designed has a simple structure and is easy to configure. And the absorption material has high average absorption rate and a wide absorption bandwidth. We therefore believe that the metamaterial absorption material has great application prospects in optoelectronic detection, infrared imaging and infrared stealth.

Near-infrared detection based on the excitation of hot electrons in Au/Si microcone array

Although the photoresponse cut-off wavelength of Si is about 1100 nm due to the Si bandgap energy, the internal photoemission effect (IPE) of the Au/Si junction in Schottky detector can extend the absorption wavelength, which makes it a promising candidate for the Si-based infrared detector. However, due to low light absorption, low photon–electron interaction, and poor electron injection efficiency, the near-infrared light detection efficiency of the Schottky detector is still insufficient. The synergistic effect of Si nano/microstructures with a strong light trapping effect and nanoscale Au films with surface plasmon enhanced absorption may provide an effective solution for improving the detection efficiency. In this paper, a large-area periodic Si microcone array covered by an Au film has successfully been fabricated by one-time dry etching based on the mature polystyrene microspheres lithography technique and vacuum thermal deposition, and its properties for hot electron-based near infrared photodetection are investigated. Optical measurements show that the 20 nm-thick Au covered Si microcone array exhibits a low reflectance and a strong absorption (about 85%) in wide wavelength range (900–2500 nm), and the detection responsivity can reach a value as high as 17.1 and 7.0 mA W−1 at 1200 and 1310 nm under the front illumination, and 35.9 mA W−1 at 1310 nm under the back illumination respectively. Three-dimensional finite difference time domain (3D-FDTD) simulation results show that the enhanced local electric field in the Au layer distributes near the air/Au interface under the front illumination and close to the Au/Si interface under the back illumination. The back illumination favors the injection of photo-generated hot electrons in Au layer into Si, which can explain the higher responsivity under the back illumination. Our research is expected to promote the practical application of Schottky photodetectors to Si-compatible near infrared photodetectors.

Magnetic field effects on electronic and optical properties in variant toroidal quantum ring: A comparative study of GaN, GaAs, and CdSe materials

In this work, we have examined the electronic and optical properties of three Variant Toroidal Quantum Ring (VTQR) materials, GaN, GaAs, and CdSe, in the presence of an axial magnetic field. Using an infinite potential model and based on the effective mass approximation, we calculated eigenvalues and eigenvectors using the three-dimensional finite difference method. This research aims to improve our understanding of the impact of the magnetic field on VTQRs of different sizes fabricated from various materials, such as GaAs, GaN, and CdSe. We simultaneously studied the geometrical parameters of VTQR nanostructures and the influence of the axial magnetic field on electronic energy, donor energy, electron-donor binding energy, magnetic shift, diamagnetic susceptibility, bandgap energy, and optical band gab. Our results show a strong correlation between electron-impurity binding energy, geometric parameters, and the presence of a magnetic field. CdSe consistently displays the highest binding energy, indicating superior stability under the study conditions. The effects of the magnetic field on these materials vary, with CdSe exhibiting increased sensitivity and GaAs demonstrating the lowest sensitivity. Nanostructure dimensions, including radii and curvature angles, play a central role in modulating the effects of binding energy and magnetic field, reflecting distinct electronic properties.

Impact of combined electric and magnetic fields on the physical properties of GaAs variant quantum ring quarter cross-section in presence of an off-center shallow donor impurity

In this study, we explored the complex effects of electric fields in three unique directions and axial magnetic field on a GaAs-Variant Quantum Ring Quarter Cross-Section (VQRQCS), particularly when there is an off-center shallow donor impurity. The investigation explores the impact of these fields on various physical attributes, including electronic energy, binding energy, magnetic shift, Stark shift, average electron impurity distance, and diamagnetic susceptibility. Using effective mass approximation and three-dimensional finite difference methods we solved the Schrodinger equation. Our result shows that the geometric radius of the VQRQCS has an essential impact on electronic energy. Notably, as the radius increases, the electronic energy decreases, regardless of the presence of fields. In particular, we found that magnetic fields amplify the electronic energy of the ground state. The angle of curvature of the nanostructure and the direction of the electric field also play an important role. Additionally, the electron–impurity binding energy decreases with the growth of the nanostructure, with external fields intensifying this effect. The average distance between the electron and the impurity, analyzed in the context of simultaneously applied fields, provides insight into the Coulomb interaction. Diamagnetic susceptibility, measuring the response of a material to an external magnetic field, is studied, indicating opposition to the external field. In summary, this research highlights the nuanced interactions between electric and magnetic fields that determine the properties of a GaAs quantum ring, providing critical insights for quantum ring-based technological advancements.

Numerical Simulation Study on the Influence of Fracture on Borehole Wave Modes: Insights from Fracture Width, Filling Condition, and Acoustic Frequency.

Unconventional reservoirs, such as shale and tight formations, have become increasingly vital contributors to oil and gas production. In these reservoirs, fractures serve as crucial spaces for fluid migration and storage, making their precise assessment essential. Array acoustic logging stands out as a pivotal method for evaluating fractures. To investigate the impact of fracture width, fracture-filling conditions, and acoustic frequency on compressional and shear waves, a three-dimensional variable mesh finite difference program was employed for acoustic logging numerical simulation. Firstly, numerical models representing fractured formations with varying fracture widths and distinct fluid-filling conditions were established, and array acoustic logging numerical simulations were conducted at different frequencies. Subsequently, the waveform data were processed to extract acoustic characteristic parameters, such as velocities and amplitude attenuations of compressional and shear waves. Finally, a quantitative analysis was conducted to examine the variation patterns of characteristic parameters of refracted compressional and shear waves in relation to fracture properties. The research results indicate that amplitude attenuation information derived from borehole wave modes is particularly sensitive to the changes in fracture properties. As fracture width increased, we observed a significant amplitude attenuation in both compressional and shear waves, proportional to the logarithm of the attenuation coefficients. Furthermore, when the fracture width was constant, gas-filled fractures exhibited more prominent amplitude attenuation than water-filled fractures, with shear wave attenuation being more sensitive to the filling material. Moreover, from a quantitative perspective, the analysis revealed that the attenuation coefficients of refracted compressional and shear waves exhibited an exponential variation with gas saturation. Notably, once fracture width and filling conditions were established, the amplitudes of compressional and shear waves at the dominant frequency of 40 kHz were significantly reduced compared to those at 8 kHz, accompanied by increased attenuation. Subsequent quantitative analysis revealed that, when the product of fracture width and dominant frequency remains constant, the corresponding attenuation coefficient ratios approach 1. This indicates that the attenuation process of acoustic propagation in fractured media follows the principle of acoustic similarity. The findings of this study provide reference for further research on fracture property evaluation methods based on array acoustic logging data.

A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

A low loss silicon waveguide bend based on width and curvature variations

A simple, low loss and compact 90° SOI waveguide bend constructed by using an inner circular curve and an outer Euler-circular curve was proposed, optimal designed and fabricated. By adopting this simple structure, the width and curvature of the waveguide bend can be varied simultaneously, which can effectively suppress both the mode mismatch loss and the radiation loss. Three-dimensional finite difference time domain simulation results indicate a very low excess loss of about 0.0056 dB can be achieved for equivalent bending radius of 2 μm. By using the cut-back method, a low loss of about 0.0175 dB at 1550 nm was measured, which is less than one quarter of the traditional circular bend. In addition, the wavelength dependence for the proposed SOI waveguide bend was investigated and 0.0088 dB–0.0247 dB was measured in the wavelength range of 1480∼1580 nm.

Excavation method optimization and mechanical responses investigating of a shallow buried super large section tunnels: a case study in Zhejiang

The construction of super large section (SLS) shallow buried tunnels involves challenges related to their large span, high flat rate, and complex construction process. Selecting an appropriate excavation method is crucial for ensuring stability, controlling costs, and managing the construction timeline. This study focuses on the selection of excavation methods and the mechanical responses of SLS tunnels in different types of surrounding rock. The research is based on the Yangjiashan tunnel project in Zhejiang Province, China, which is a four-line highway tunnel with a span of 21.3 m. Three sequential excavation methods were proposed and simulated using the three-dimensional finite difference method: the “upper first and lower later” side drift (SD) method, the central diaphragm method, and the top heading and bench (HB) method. The mechanical response characteristics of tunnel construction under these methods were investigated, including rock deformation, rock pressure, and the internal forces acting on the primary support. By comparing the performance of the three construction methods in rock masses of Grades III to V, the study aimed to determine the optimal construction method for SLS tunnels considering factors such as safety, cost, and schedule. Field tests were conducted to evaluate the effectiveness of the optimized construction scheme. The results of the field monitoring indicated that the “upper first and lower later” SD method in Grade V rock mass and the HB method in Grade III to IV rock mass are feasible and cost-effective under certain conditions. The research findings provide valuable insights for the design and construction of SLS tunnels in complex conditions, serving as a reference for engineers and project managers.

Shaking Table Testing and Numerical Study on Aseismic Measures of Twin-Tube Tunnel Crossing Fault Zone with Extra-Large Section

As transportation networks continue to expand into mountainous regions with high seismic activity, ensuring the seismic safety of tunnels crossing active faults has become increasingly crucial. This study aimed to enhance our understanding of the impact of fault zones on the seismic behavior of tunnels and to provide optimized seismic design recommendations through a comprehensive experimental and numerical investigation. The focus of this research is the Xiangyangshan Highway Tunnel in China, which intersects a significant longitudinal fault. Large-scale shake table tests were performed on 1:100 scale physical models of the tunnel to analyze the seismic responses under various ground motion excitations. Detailed three-dimensional finite difference models were developed in FLAC3D and calibrated based on the shake table results. The tests indicated that strains, earth pressures, and accelerations experience localized amplification within 10–20 m of the fault interface compared to undisturbed ground sections. Common seismic mitigation measures, such as rock grouting, seismic joints, and shock absorption layers, were observed to effectively reduce the amplified seismic demands. Grouting, in particular, led to an average reduction of up to 56.3% in circumferential strain and 38.5% in earth pressure. It was concluded that 6 m thick grouted zones and 20 cm thick rubber interlayers between tunnel lining shells provide optimal structural reinforcement against the effects of fault zones. This study provides valuable insights for improving the seismic resilience of underground transportation corridors in seismically active regions.

Seismic Structure-Soil-Structure Interaction (SSSI) between piled neighboring bridges: Influence of height ratio

Abstract This paper explores the impact of height ratios on the seismic Structure-Soil-Structure Interaction (SSSI) for three adjacent bridges with varying superstructure masses (Mst = 350, 1050, 350 t) through 3D numerical simulations. A comprehensive series of numerical analyses has been conducted across different height ratios (R = 1, 1.1, 1.15, 1.2, 1.25, 1.5, 2, and 3) to assess their influence on superstructure acceleration and the internal forces within the foundation piles. The bridges under investigation are supported by groups of piles embedded in nonlinear clay. The numerical simulations were executed using fast Lagrangian analysis of continua in three dimensions (FLAC 3D), a three-dimensional finite differences modeling software. The findings revealed that variations in mass ratios significantly impact the SSSI effects on superstructure acceleration and pile internal forces. Notably, adverse effects were more pronounced for mass ratios of R = 1.1 and 1.2, leading to an increase in bending moment, shear force, and superstructure acceleration by up to 237.8%, 291.4%, and 70.33%, respectively. In contrast, a mass ratio of R = 3 resulted in a decrease in bending moment, shear force, and superstructure acceleration by up to 72%, 82.14%, and 81.13%, respectively. This implies that a careful arrangement of adjacent structures with different masses can be employed effectively to manage the (SSSI) effects.

Numerical study on stability of geosynthetic-encased stone column-supported embankments based on equivalent method

The application of geosynthetic-encased stone column-supported embankments (GESC-supported embankments) has garnered significant attention in geotechnical engineering, with limited investigations into their slope stability. In this paper, an equivalent method was proposed to establish GESC-supported embankment models through three-dimensional finite difference method (3D-FDM). Responses of factor of safety (FS) to arrangement tightness of GESCs (e.g., various column diameters, spacings, and quantities under constant area replacement ratio) and hoop effect of geosynthetic encasements (e.g., various geogrid strengths under different shear strengths of soft soil) were studied. For a given area replacement ratio, FS increased non-linearly with the increasing column quantity or the decreasing ratio of column spacing to diameter at high area replacement ratios. GESCs with smaller diameter and spacing proved to be more effective in improving slope stability, and an optimum ratio of column spacing to diameter was observed for practical use. Besides, FS increased linearly with geogrid strength at low geogrid strength levels, but an extremely lack of the shear strength of soft soils or the column quantity was unfavorable for the application of GESCs. Bending failure was the primary failure feature of GESCs under embankment loading, and the geogrid strength influenced slope stability through the bending capacity of GESCs.